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Acta Sinica Quantum Optica

The Quantum Effects of Double Mode Mesoscopic Transmission Line in Excited Coherent State

Zhongchu Wang

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The standing wave field in a mesoscopic transmission line is regarded as the superposition of two traveling waves having the same frequency and trave ling in opposite direction. The double mode photon field with the same frequency is given by quantizing the transmission line. An analysis is made for the quant u m fluctuations of the voltage and current gradient of the line in excited cohere nt state,and the difference between the double mode transmission line and LC cir cuit , the double mode and single mode transmission line is discussed.

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The standing wave field in a mesoscopic transmission line is regarded as the superposition of two traveling waves having the same frequency and trave ling in opposite direction. The double mode photon field with the same frequency is given by quantizing the transmission line. An analysis is made for the quant u m fluctuations of the voltage and current gradient of the line in excited cohere nt state,and the difference between the double mode transmission line and LC cir cuit , the double mode and single mode transmission line is discussed.
A mesoscopic parallel LC circuit model with double dissipative branch circuits is put forward according to the actual situation of the circuit.It is quantized with the theory of the classical circuit and the quantization method of damped harmonic oscillator.Then the quantum fluctuations of the voltage and the current of the circuit in vacuum state and the quantum fluctuations affected by the dissipative resistances are discussed.The results show that the quantum fluctuations of the voltage and the current of both branches are not only related with the parameters of the LC circuit components,but also affected by the dissipative resistances.They decay with the same exponential with time.The coefficients of the quantum fluctuations of the current are the same,while those of the voltage are different.When the two dissipative resistances are equal,the quantum fluctuations of the voltage and the current of both branches take on the same behavior respectively.
By making use of thermo-field dynamics (TFD), the quantum fluctuations of current of the mesoscopic lossless transmission line in the vacuum state, the coherent states and the squeezed states with thermal noise have been studied. Thus the dependence of the fluctuations on temperature in these states at finite temperature can be seen. It is shown that the quantum fluctuations depend on not only the parameters of the transmission line but also the environmental temperature T. The higher the temperature, the more quantum noise the line exhibits.
We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting witha single-mode quantized travelling-wave laser field in a double-well potential. When the atom-field system is initiallyin a coherent state, expressions for the energy exchange between atoms and photons are derived. It is revealed thatatoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included. It is found that there is an alternating current with twodifferent sinusoidal oscillations between the two wells, but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field, both the population difference and the atomic tunnellingcurrent are only a single oscillation. But they will respectively become a superposition of two oscillations with differentoscillatory frequencies in the presence of the laser field. For the two oscillations of the population difference, one alwayshas an increment in the oscillatory frequency, the other can have an increment or a decrease under different cases. Theseconclusions are also suitable to those of the atomic tunnelling current. As a possible application, by measurement of theatomic tunnelling current between the two wells, the number of Bose-condensed atoms can be evaluated. lBy properlyselecting the laser field, the expected atomic tunnelling current can be obtained too.
The superposition of excited double-mode SU(2) coherent state |ψ=Cm(|M,ξ;m+ei|M,ξ*;m) is constructed and its quantum statistical properties are investigated with numeric method.The results exhibit that when the photons are added to the mode b of the double mode SU(2) coherent state,the two field modes can preserve anti-relation character,and presents a special effect of light amplification;the sub-Poissonian photon statistics properties of mode b is obvious enhanced and that of mode a is slightly weakened;anti-bunching effect of two modes of field are all enhanced,but as the quantum number of excitation m is increased,the anti-relation character of the two modes of field is weakened.